149 citations · 710 across the 38 of their papers we have counts for
9 papers · 1 filter
Coarse embeddings of products of trees as quasi-isometry invariants
Mark Hagen, Alessandro Sisto
We consider the maximal number of factors of a product of bushy trees that can be quasi-isometrically, or even coarsely embedded into various groups of interest, including mapping…
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Carolyn Abbott, Mark Hagen, Harry Petyt +1
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic gr…
Homotopy equivalent boundaries of cube complexes
Talia Fernós, David Futer, Mark Hagen
A finite-dimensional CAT(0) cube complex is equipped with several well-studied boundaries. These include the Tits boundary (which depends on the CAT(0) metric), the Roller boun…
Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms
Mark Hagen, Jacob Russell, Alessandro Sisto +1
Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a hierarchically hyperbolic space structure. However, these structures were not always equivariant with respect t…
Deforming cubulations of hyperbolic groups
Elia Fioravanti, Mark Hagen
We describe a procedure to deform cubulations of hyperbolic groups by "bending hyperplanes". Our construction is inspired by related constructions like Thurston's Mickey Mouse exam…
Quasiflats in hierarchically hyperbolic spaces
Jason Behrstock, Mark F Hagen, Alessandro Sisto
The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the…
Boundaries and automorphisms of hierarchically hyperbolic spaces
Matthew G. Durham, Mark F. Hagen, Alessandro Sisto
Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichmüller space, right-angled Artin groups, and many other…
Hierarchically hyperbolic spaces I: curve complexes for cubical groups
Jason Behrstock, Mark F. Hagen, Alessandro Sisto
In the context of CAT(0) cubical groups, we develop an analogue of the theory of curve complexes and subsurface projections. The role of the subsurfaces is played by a collection o…
Cocompactly cubulated graph manifolds
Mark F. Hagen, Piotr Przytycki
Let M be a graph manifold. We show that π_1M is the fundamental group of a compact nonpositively curved cube complex if and only if M is chargeless. We also prove that in that case…